semc
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Hi, I am trying to plot a function subjected to a nonlinear wave equation. One of the method I found for solving the nonlinear Schrödinger equation is the split step Fourier method. However I noticed that this method only works for a specific form of PDE where the equation has an analytic solution for both the linear and nonlinear part. So how do I solve numerically any arbitrary PDE? Specifically, my PDE is
[itex]\partial_zE(r_⊥,z,\tau)-∇^2_⊥\int^{\tau}_{-\infty}d\tau 'E(r_⊥,z,\tau ')=\int^{\tau}_{-\infty}d\tau '\omega^2(r_⊥,z,\tau ')-\frac{\partial_{\tau}n(r_⊥,z,\tau)}{E(r_⊥,z,\tau)}[/itex]
and I want to solve for the evolution of E. Any help would be greatly appreciated. Thanks!
[itex]\partial_zE(r_⊥,z,\tau)-∇^2_⊥\int^{\tau}_{-\infty}d\tau 'E(r_⊥,z,\tau ')=\int^{\tau}_{-\infty}d\tau '\omega^2(r_⊥,z,\tau ')-\frac{\partial_{\tau}n(r_⊥,z,\tau)}{E(r_⊥,z,\tau)}[/itex]
and I want to solve for the evolution of E. Any help would be greatly appreciated. Thanks!